Staff at the Christian Legal Centre announced that have asked the European Court of Human Rights (ECHR) to consider the case of Alfie Evans for a second time, on behalf of his parents.
Andrea Williams, chief executive of the Centre, which is now representing Alfie's family, said: "We are going to appeal to the ECHR hoping we can stay the end of life order our courts have made."
The development comes after the UK's Supreme Court refused on Friday to consider the case of Tom Evans and Kate James for a second time. The couple previously lost a second challenge over their child at the Court of Appeal.
Three justices from the most senior court in the country concluded there is "no hope" in the 23-month-old getting better and there is "no reason for further delay" in medical staff implementing an end-of-life care plan.
The judges decided Alder Hey Children's Hospital in Liverpool "must be free to do what has been determined to be in Alfie's best interests".
Tom Evans and Kate James have received an invitation from the Pope - who tweeted his support for Alfie earlier this month - to take the toddler to a Vatican-run children's hospital in Rome for further treatment.
In a statement, Mr Evans said: "We will not give up.
"We will continue to fight, by all means available to us within the law, to save our son's life."
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